PPT Mass, Weight, and Gravity
Developer Notes 1. There are some activities here that could be filled out.
Version Date Who Revisions 06 20040109 dk . Reformatted . Added G to instruction .
Goals 1. Students should understand that gravity is the force of attraction between two objects. 2. Students should understand that all objects have gravity, and the more mass an object has, the more gravity it has. 3. Students should understand that the force of gravity decreases as the inverse square of the distance between the objects. 4. Students should understand the difference between mass and weight. 5. Students should understand that weight is a force. 6. Students should be able to calculate the weight of an object in Newtons, given its mass and the acceleration of gravity. 2 7. Students should be able to use the formula F = Gm1m2/d to calculate the force of gravity between two objects. 8. Students should understand why all object fall at the same rate (in the same gravitational field, neglecting air resistance).
Concepts & Skills Introduced
Area Concept physics mass physics weight 2 2 physics gravity, F m1m2/d , F = Gm1m2/d math inverse square relation
Time Required
Warm-up Questions . What is gravity? . How can you find the mass of something? . What is weight? . Explain mass and weight and the differences between them. . Why would the same object weigh less on the moon than on Earth?
Presentation This activity is a follow-up to the Newton's 2nd activity. By the end of that activity, students
should be comfortable with Fnet = ma. They should also know that the force causing the cart to move was gravity acting on the hanging mass. Here we expand a little and look at mass and weight.
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The main thing about gravity is that all objects have it, just like all objects have mass and inertia - gravity is a property of matter. All objects are attracted to each other. The strength of gravity is proportional to the mass of the object. If an object's mass doubles, the force of gravity on it doubles. The force of gravity depends on the mass of both of the objects that attract each other. If the mass of either one doubles, the force doubles.
Like many other things (light, sound, magnetism), the strength of gravity decreases with the inverse square of the distance between the objects.
The force of gravity (gravitational force) causes you to accelerate down (toward the center of the earth) - if someone pulls your chair out from under you, you'll accelerate quickly to the floor! When you're sitting in your chair (or on the floor), the force of gravity would make you accelerate, but the chair (or floor) gets in the way. You don't move because the net force on you is zero, hence the net acceleration is also zero. Force tends to cause a change in motion (acceleration)!
Cavendish's and von Jolly's experiments to determine G are fun to discuss. Cavendish used a delicate torsion balance to measure the pull between two pieces of lead. von Jolly used a beam balance with a flask of mercury on one side, then rolled a 6 ton ball of lead (about 1 m diameter) under the mercury and measured the change in the balance. It's quite an image.
Extra material: Gravity is very weak in comparison to the other three fundamental forces (electromagnetic, strong nuclear, weak nuclear, which are now considered to be the same), but it works over the longest distance. While gravity causes attraction between like objects, electromagnetic force causes attraction between unlike particles and repulsion between like particles. At long distances, the pluses and minuses at the atomic scale blur together to look like zero charge, while gravity still looks the same. That is why it operates at long distances. At very short distances, the pluses and minuses at the atomic scale become more obviously separate from each other, so electromagnetic forces tend to dominate. That's why you don't fall through the earth.
Assessment
Writing Prompts 1.
Relevance
Answers to Exercises . F = ma F = 1 kg 9.8 m/s2 F = 9.8 N . Multiply your mass in kg times 9.8 m/s2. . Multiply your mass in kg times 1.6 m/s2. Your mass on the moon would be the same as your mass on Earth.
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. Multiply your mass in kg times 25 m/s2. Your mass on Jupiter would be the same as your mass on Earth. . Shake both boxes, or accelerate them somehow. The one that is harder to accelerate is the full (heavier, more massive) one. . If you were three times as far from the center of the earth, the gravitational attraction would be (1/3)2 (or 1/9) as strong, so the gravitational force on you would be 100 N. . The force of Earth's gravity on the astronaut would be closer to 800 N. . In orbit, you would exert no force on a scale. Acceleration is relative (just like motion). In orbit, you and the scale accelerate (fall) at the same rate. On Earth, the scale is held still - if you step off of it, you will accelerate to the floor. In a weightless condition, if you step off of the scale, you won't move relative to it. . Yes, there's a gravitational attraction between a person and a chair. But there's a greater gravitational attraction between Earth and the chair, so the chair sticks to the earth, not the person. . The person weighs 500 N = 50 kg 10 m/s2. In the second picture, Earth weighs 500 N. Weight is a measure of the gravitational force between two objects.
Answers to Challenge/ extension 9. 9,401 N. The force would be less by the ratio of the distances squared. 10. This should equal your weight in N, as calculated in #2 above.
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Background Many things get weaker the further you are away from them. One example is light. The further you are from the light, the dimmer it appears. Other things act in a similar way: sound, heat, magnetic force, electric force, and gravitational force. All of them get weaker with distance, but what is the pattern?
Problem Figure out the rate at which light intensity decreases with distance.
Materials 1 light 2 sheets of 1/4" graph (quadrille) paper 1 metric ruler or meter stick 1 cutting instrument (razor? knife? scissors?)
Procedure Setup 1. Work in groups of two. 2. Cut a 1/4" flap in one of the pieces of graph paper. Set up your materials so that the light can shine straight through the paper with the hole (flap) and onto the target paper. Data gathering 1. Note how bright the light is shining on the flap. Now open the flap and let the light go through onto the target paper. a. Is the light on the target paper brighter, dimmer, or the same? b. Is the area of light on the target paper bigger, smaller, or the same size as the hole? 2. Change the setup so that the light on the target paper covers exactly 4 squares. Measure the distance from the bulb to the hole and the distance from the bulb to the target paper. 3. Repeat for an area of 9 squares and 16 squares.
Summary 1. What's the pattern? a. Express the pattern in words. b. Express the pattern mathematically. 2. Predict a setup so that the light on the target paper covers 25 squares, and try it. 3. What happens to all of the light that would hit the target paper when the flap is closed? 4. How do you think the intensity of the light on the target paper compares to the intensity of light on the flap?
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Background
Problem Investigate doubling the mass to see if it doubles the gravitational force. This would be very easy. Just hang a mass on a spring scale, then add a second identical one. Does the scale go twice as far? What if the mass of Earth doubled (but it stayed the same size)? This almost has to come after the students have seen the exercise with Earth and a person weighing each other.
Materials
Procedure
Summary
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Reading Everybody knows you fall down because of gravity. But what is gravity?
Prior to Newton, most people thought gravity only existed on Earth. They believed that the stars, moon, and sun operated by different laws from objects on Earth. Newton saw that the moon orbits Earth for the same reason that an apple falls from a tree - it is pulled to Earth by gravity. He said that all objects, in the heavens or on Earth, act by the same laws. This is the Newtonian synthesis.
Newton went further and created his Law of Universal Gravitation, shown below.
Mass is a property of matter (stuff). Anything that has mass has inertia. Anything that has mass also has gravity. The more mass an object has, the more gravity it has (just like it has more inertia).* All objects are attracted to each other by gravity. Because the force of gravity reaches everywhere, everything always has force on it. (Sometimes the net force is zero.)
The amount of gravity is directly proportional to the amount of mass. If the object's mass doubles, the gravitational force on it doubles.
F m1 The gravitational force between two objects is directly proportional to the masses of both objects. If either object's mass doubles, the force between them doubles.
F m1m2 (note that F = m1 + m2 doesn’t work) Like light and sound, gravity gets weaker as you get further away. But if you go twice as far away, the gravity isn't just half as much, it's one quarter as much. The gravitational force gets weaker proportional to the inverse square of the distance between the two objects. The distance is the distance between their centers of mass. F 1/d2 Put the two together, and you have Newton's Law of Universal Gravitation.
Every body in the universe attracts every other body with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two bodies. 2 F m1m2/d
The constant of proportionality was later determined experimentally. It is called G. G = 6.710-11 m3/(kgs2) You can use G to calculate the gravitational force between two objects if you know their masses and the distance between their centers of mass. 2 F = Gm1m2/d 2 2 The units for G work with m1m2/d so that when they're multiplied, the result is kgm/s , or N.
G is a very small number, and gravitational forces are weak, especially if the two masses are small. For example, there is a gravitational attraction between this paper and you, but it is much, much weaker than the gravitational attraction between the paper and Earth, so the paper falls down rather than sticking to you.
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When you stand on a scale, the scale measures the force of attraction between you and Earth. F = ma. Your weight is your mass times the acceleration of gravity: F = mg. So weight is not the same as mass. Weight is a force. It changes depending on the strength of gravity. Mass does not change.
Why do all objects fall with the same acceleration (neglecting air resistance)? Think about it. An object with twice the mass will have twice as much force (weight) accelerating it down. But it will also have twice as much inertia resisting acceleration. The two cancel each other, so the object falls at the same rate as an object with less mass. The acceleration of a falling object is equal to the force pulling it down divided by its inertia, a = F/m But what is the force pulling the object down? It is the object's mass times the acceleration due to gravity, F = mg Substitute mg for F in a = F/m, and you get a = mg/m The m's cancel out, so the acceleration is just g. The amount of mass doesn't matter.
*(Extra material: Einstein posited that inertial mass and gravitational mass are identical. This means that inertia and gravity are the same. We think of objects traveling in a straight line due to their inertia, but they actually travel in curved paths due to gravity, like Earth orbiting the sun. This led Einstein to say that space is curved - a curve is the shortest distance between two points in curved space-time.)
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Exercises 1. Describe mass, inertia, and gravity, and the differences between them. 2. What is weight, and how does it differ from mass? Explain in words and a formula. 3. What is the force of gravity on a 1 kg mass on Earth? 4. If the mass of an object doubles, what happens to its weight? Why? 5. Gravitational force from the moon causes tides on Earth. Does gravity from the sun reach Earth? How can you tell? 6. What is your mass? Calculate your weight in Newtons on Earth. 7. How much force would you exert on a scale on the moon? (The acceleration due to gravity on the moon is 1.6 m/s2.) What would your mass be on the moon? 8. What would your weight be on Jupiter? (The acceleration due to gravity on Jupiter is 25 m/s2.) What would your mass be on Jupiter? 9. Imagine yourself in space in a weightless situation. You have two identical looking boxes. One is full and one is empty. How can you tell which is which without opening them? 10. If Earth had the same mass, but was twice as big (twice the diameter), how much would you weigh? Why? 11. If your weight on Earth is 900 N, what would the force of gravity on you be if you were three times as far from the center of Earth? Why? 12. You have seen pictures of astronauts in a weightless condition in space stations. Space stations orbit Earth at an altitude of about 200 km in order to avoid air resistance. The radius of Earth is 6,371 km. If the force of gravity on an astronaut on the ground is 800 N, would the force of gravity on the astronaut in orbit be closer to 0 N or 800 N? 13. If you were in orbit, how much force would you exert on a scale? Why? 14. Is there a gravitational attraction between you and your chair? Then why doesn't it stick to you when you stand up? 15. Earth has a mass of 6.01024 kg. In the picture, the person has a mass of 50 kg. The scale measures in Newtons. How much does the person weigh? In the second picture, how much does Earth weigh? Explain.
Earth
Earth
16. Would an object take the same amount of time to fall 5 m on Earth and on the moon? Explain. 17. How long would a ball take to fall 5 m on Earth? How long would it take on the moon? How long on Jupiter? (Neglect air resistance.) 18. How fast would the ball be going after 5 m on Earth, the moon, and Jupiter?
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19. If you had two balls that were the same shape, but one was made of steel and one was made of lightweight foam, and you dropped them from a high place, which would hit the ground first? Which would hit the ground first if there was no air resistance? Why?
Challenge/ extension 1. The radius of Earth is 6,371,000 m. Satellites circle Earth at an altitude of about 200,000 m in order to be outside the atmosphere. If the force of gravity on a satellite on the ground is 10,000 N, what would the force of gravity on it be at an altitude of 200,000 m? 2. The mass of Earth is 6.01024 kg. Calculate the force of attraction between you and Earth. 2 3. If you divide both sides of F = Gm1m2/d by m2, what does that leave in place of F? 2 Calculate Gm1/d for Earth (m1 is the mass of Earth). 4. Find out why the same side of the moon always faces Earth. 5. Compare the gravitational force on you of your friend 1 m away, and of Mars. Mars has a mass of 6.41023 kg, and, at its closest, it is about 71010 m from Earth.
Vocabulary Gravity - a property of matter. The force of attraction between all objects with mass. (Gravity is one of two fundamental forces.) g - the acceleration due to gravity on Earth, 9.8 m/s2 G - the gravitational constant. It is 6.710-11 m3/(kgs2). Mass - the amount of material in an object. All objects with mass have inertia and gravity. . Newton's Law of Universal Gravitation. Every body in the universe attracts every other body with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two bodies. 2 F m1m2/d Weight - the force on an object due to the gravitational attraction of another object (like Earth). Weight is measured in Newtons (pounds in the US system).
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